Higher-order symmetric duality in nondifferentiable multiobjective fractional programming problem over cone contraints

Ramu Dubey,Deepmala Deepmala,Vishnu Narayan Mishra

doi:10.19139/soic-2310-5070-601

Abstract

In this paper, we introduce the definition of higher-order K-(C, α, ρ, d)-convexity/pseudoconvexity over cone and discuss a nontrivial numerical examples for existing such type of functions. The purpose of the paper is to study higher order fractional symmetric duality over arbitrary cones for nondifferentiable Mond-Weir type programs under higher- order K-(C, α, ρ, d)-convexity/pseudoconvexity assumptions. Next, we prove appropriate duality relations under aforesaid assumptions.

Highlights

Convexity and generalized convexity have been playing an important role in developing optimality and duality results for multiobjective programming problems which are mathematical models for most of the real world problems occuring in the fields of engineering, economics, finance, game theory etc
In Chen [2] multiobjective fractional problem and its duality relations have been considered under higher-order (f, α, ρ, d)- convexity assumptions
Ying [5] has studied higher-order multiobjective symmetric fractional problem and formulated its Mond- Weir type dual and duality theorems are proved under the higher-order (f, α, ρ, d)-convexity assumptions

Summary

Introduction

Convexity and generalized convexity have been playing an important role in developing optimality and duality results for multiobjective programming problems which are mathematical models for most of the real world problems occuring in the fields of engineering, economics, finance, game theory etc. Mangasarian [1] formulated higher-order dual for a single objective nonlinear problems,{minf (x), subject to g(x) 0} Motivated by this concept, many researchers have worked in this direction. Kassem [3] have been studied higher-order vector optimization problem and derived duality results under generalized convexity assumptions. Suneja et al [4] proved higher-order Mond-Weir and Schaible type nondifferentiable dual programs and their duality relations under higher-order (f, ρ, σ) -type I- assumptions. Ying [5] has studied higher-order multiobjective symmetric fractional problem and formulated its Mond- Weir type dual and duality theorems are proved under the higher-order (f, α, ρ, d)-convexity assumptions. We formulate a pair of nondifferentiable multiobjective Mond-Weir type higher-order symmetric fractional programming problems over arbitrary cones. We establish appropriate duality theorems under higher-order K-(C, α, ρ, d) convexity/pseudoconvexity assumptions followed by conclusions

Preliminaries

Higher-order Mond-Weir fractional symmetric duality

Conclusion